Related papers: Non-normal logics: semantic analysis and proof the…
We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new…
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…
This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de…
This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…
Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with…
We consider modal logic extended with the well-known temporal operator 'eventually' and provide a cut-elimination procedure for a cyclic sequent calculus that captures this fragment. The work showcases an adaptation of the reductive…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
We define and study translations between the maximal class of analytic display calculi for tense logics and labeled sequent calculi, thus solving an open problem about the translatability of proofs between the two formalisms. In particular,…
We present a proof system for a multimodal logic, based on our previous work on a multimodal Martin-Loef type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e. a small 2-category.…
We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use…
This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After…
This paper investigates the extension of lattice-based logics into modal languages. We observe that such extensions admit multiple approaches, as the interpretation of the necessity operator is not uniquely determined by the underlying…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
Systems of deontic logic suffer either from being too expressive and therefore hard to mechanize, or from being too simple to capture relevant aspects of normative reasoning. In this article we look for a suitable way in between: the…
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…
This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to…
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…
In the present paper syntax and semantics will be presented for an expansion of ordinary n-agent QML with constant domain, non-rigid constants, rigid variables and including both functions, relations, and equality. Further, the number of…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…